You know this is not something extra for fans....This is something that just happens.
Whatever weapon you have should always appear in cutscenes, because the cutscene are usually evented, meaning that a series of processes activate when the player touches a certain something or goes on to a certain area of the map. Since the selected keyblade is part of the characters character model at that point in time as an addition, it will appear in the event unless the event changes the weapon for you.
In the case that a different weapon than the one you have equipped appears it means that this cutscene is NOT evented, and has been prerecorded. That is why in theater mode, the character's base keyblade is usually shown. Because those cutscenes have been prerecorded for the sake of theater mode.